Hmm, I think I’d say (with a free version provided if one exists):
- Edith Hamilton. Mythology. It’s a really good handbook when you don’t know anything about Greek myths or their characters. It gives a good overview of different stories and a summary of the Trojan War (if you don’t feel like you’re ready to tackle the Iliad right in the beginning, this book is a good place to start), and the stories of the most important (half)mortal families of Greek mythology. Basically, it’s a wonderful book and I love it and EH is my hero.
- Hesiod. Theogony. Talks about the creation of the universe and the genealogy of the gods.
- Euripides. Medea. It is quite different from Seneca’s version, but really good nonetheless. And Bacchae, which gives a good insight to the god Dionysus and the consequences of invoking the wrath of a god.
- Aeschylus. Agamemnon. It’s the first part of the Oresteia and it’s really interesting to read.
- Sophocles. Oedipus Rex. Gives a really good insight to how the Greeks viewed fate and its inevitability.
- Homer. The Iliad and The Odyssey. Both are part of the Epic Cycle, and related to the events of the Trojan War.
- Proclus. Summary of the Epic Cycle. It’s from a later period, but it gives a short summary of the lost works of the Epic Cycle, which was a collection of epic poems related to the Trojan War.
- And finally, something that isn’t precisely classical Greek mythology but since I’m a Romantic at heart: the poetry of John Keats. Like seriously, his work is really closely connected to Greek myth and I love him so much.
Half of this list is Greek tragedies and they aren’t very long, so they’re as good a place to start as any.
If you don’t know whether you’re capable of getting into Theogony or the epics right away, you can absolutely leave them to the last, because if you read Mythology first then you should at least have a general knowledge of what’s going on in them.